Electronic Structure For Nanosystems Of A Few Dirac Electron Materials

The two-dimensional Dirac electron systems, such as graphene and its analogy of Si, Ge etc.. two-dimensional topological insulator (HgTe/CdTe quantum well), and three-dimensional topological insulator (Bi2Se3, etc.). characterize Dirac cone type of energy band in Γ piont. Its low energy effective model is described by a kind of Dirac equations, and the behaviours of electron are similar to relativistic particles, It has been a hot topic in condensed matter physics because of such spe-cial properties. The studies of such system include both aim for spin/valleytronics and important significance on foundmental science. In this thesis, we theoretically investigated gate-control and defect effects on the surface of a three-dimensional topological insulator, with comparison to traditional two-dimensional electron gas, as well as the influence of change of Fermi velocity to spin/valley polarized trans-port in ferromagnetic silicene. The purpose of all studies are for providing phys-ical basis for the design of nano-electronical devices and low-energy consumption spin/valleytronics devices in the future.The thesis is divided into six chapters. In the first chapter, we briefly introduce Spin-orbit Coupling and Quantum Spin Hall Effect, as well as the the discovery and fabrication techniques of several typical materials of two-dimensional Dirac electron system, the physical properties and their application background. In the second chapter, we provide a detailed introduction to microstructural representa-tion of mesoscopic system-local density of states(LDOS), as well as the often used methods in the study of mesoscopic quantum transport, i.e., Landauer-Buttiker formula, the transfer matrix and non-equilibrium Green function method.In the third chapter, based on the Dirac equation we study the spatial dis-tribution of electron spin polarization for a gate-controlled quai-one-dimensional channel on the surface of a three-dimensional topological insulator (3D TI). We demonstratethat an energy gap depending on channel geometry parameters is def- initely opened due to the spatial confinement, and the spin surface locking for a T-shaped channel is broken. These interesting findings for an electrically con-trolled nanostructure based on the 3D TI surface may be testable with the present experimental technique, and may provide further understanding the nature of 3D TI surface states.In the fourth chapter,by using a δ-function potential to model an atomic step line edge on the surface of a single 3D TI and a line edge between two surfaces of a 3D TI with different Fermi velocities, we have studied the decaying behavior of LDOS oscillations near and away from the edges, respectively. For the step line edge on single surface, we recover the x-3/2 power-law decaying behavior for LDOS oscillation away from the step in our model and at the same time, we found a bound state existed along the step edge as a physical realization of Tomonaga model. For a line edge, the electron refraction and total reflection are occurred at the edge, which are analogous to optics. By ignoring the influence of bound states, we show that the LDOS oscillating decay behavior in the greater Fermi velocity side is similar to that for a step line edge on a single TI surface. However, in the smaller Fermi velocity side away from the edge the LDOS oscillation shows a decaying behavior as x-1/2. and the wavevector of the LDOS oscillations is no longer equal to the diameter of the CEC of surface band but sensitively on the ratio of the two Fermi velocities.In the fifth chapter, we investigate charge, valley, and spin transports in nor-mal/ferromagnetic/normal silicene junction when the Fermi velocity is changed in ferromagnetic silicene. The change of Fermi velocity can stem from the stress of substrate and ferromagnet, or the external stretch and extrusion. We get the charge, valley/spin conductances and its polarization in this junction. The results show, by controlling the ratio on a small scale, we can get a big polarized conduc-tances. This is needful in spintronics and valleytronics. Meanwhile, we also found a universal law for this system:While keeping the spin/valley polarized conduc-tances as constants, the ratio of Fermi velocity of the normal and ferromagnetic silicene is simply proportional to the width of the ferromagnetic silicene.In chapter six, a summary of the work and a outlook are given.